Since Archimede, mathematicians tried hard to compute as many digits of Pi they could, even if it appears a useless quest to some people... But without this obsession, one must realize that we would have missed the recent discovery of several algorithms such as the product of long integers by fast fourier transform. And think about the consequences of the BBP formulas ! Thus, discover, optimize and accelerate the computation of the digits of Pi is a lively mathematical field.

Note that Havermann has a very interesting page about the fraction expansion of Pi

Digits record in a classroom

Ok, I invented this class of records ;-)... however, this was to promote the work of the 7th grade (US-equivalent) classsroom located in Bouchain, north of France. They meet every monday in this 2012-2013 year to add digits and there are 85 of them so far ! Congratulations to them !! (Click on images to get high density pictures).

Pi memory records

A Japanese holds the record, just try to imagine what it means as memory, that crazy !
Main Pi memory records:

Akira Haraguchi, a 60-year old Japanese man, managed to recite 100 000 digits of Pi in 16h30 on October 3rd, 2006, breaking his own (unofficial) record of 83 431 digits established in 2005 ! First comment from Akira: "I don't think it's anything exceptional, I just emptied my mind of everything else and recited the numbers" ;-) Here is the BBC coverage, there the world-ranking of Pi memory (not up to date) and here the report about his previous record in 2005.

About the world record of Takahashi-Kanada from april 1999 (68 719 470 000 digits)

Two computations on a HITACHI SR8000 based on two independant algorithms ( Brent/Salamin and fourth-order algorithm from the Borwein) generated 68,719,476,736 (=236) digits of Pi. Comparing the two results, they found 68,719,476,693 common digits. The new record has thus been established to 68,719,470,000 digits of Pi.

About the world record of Kanada from september 1999 (206,158,430,000 digits)

Two computations on a HITACHI SR8000 based on two independant algorithms ( Brent/Salamin and fourth-order algorithm from the Borwein) generated 206,158,430,208 (=3.2^36) digits of Pi. Comparing the two results, they found 206,158,430,163 common digits. The new record has thus been established to 206,158,430,000 digits of Pi.

About the world record of Kanada from december 2002 (1,241,100,000,000 digits)

Two computations lasting 600 hours on a HITACHI SR8000/MP with 1TB storage (1024Go), and based on two independent Machin-like formulas, generated 1,241,100,000 digits of Pi after that the result obtained in hexagesimal base was converted to base 10. Formulae used were :

This come back of amazingly simple formulae after using Brent-Salamin, Borwein algorithms or Ramanujan-like formulae for 15 years was highly unexpected. Actually, despite the algorithmic improvements, the complexity of these latter formulae had reached computer limits. Indeed, the widely use of root extractions and multiplications required the common use of very large scale Fast Fourier Transform (FFT). This algorithm needs huge memory. Kanada thus decided to be wiser and to use Machin-like formulas which need more arithmetical operations with much less very large scale FFT and so less memory. It seems that similar issues start to appear in the fastest computers in the world whose network and memory operations saturate faster than what was expected theoretically. Kanada estimates than his computation is twice faster than the previous one using Brent/Salamin and Borwein algorithms.